Comment on “Exact expression for the magnetic field of a finite cylinder with arbitrary uniform magnetization” A. Caciagli, R.J. Baars, A.P. Philipse, B.W.M. Kuipers, JMMM 456 (2018) 423–432

The magnetic field anomaly map compiled by the C. N. R. S. in 1964, which is based on profiles spaced 10 km apart and at a height of 3 km, reveals a strong positive anomaly in the central region of the western Channel. The interpretation of this type of survey is considerably facilitated by the use of transformations which permit us to present two supplementary maps: ( a ) the first derivative of the magnetic field in the vertical sense and ( b ) that of the preceding function reduced to a pole, assuming initially that magnetized bodies are created by pure induction. From these two transformations in which the effect of the magnetic substratum is considerably enhanced, we have drawn contours which represent either the principal elements of the magnetic relief or the principal ranges of magnetization of a relatively flat magnetic substratum. In the subsequent phase of interpretation, namely a comparison with the geological information available, the presence of distinct bodies of uniform magnetization was assumed. Calculations of depth indices have also been made. From the results obtained, which are synthesized in this report, we have been able to formulate a hypothesis concerning the date of the emplacement of the structures responsible for the observed anomalies.

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New compact and singularity free formulations for the magnetic field produced by a finite cylinder considering linearly varying current density

International Journal of Applied Electromagnetics and Mechanics ◽

10.3233/jae-150132 ◽

2016 ◽

Vol 50 (3) ◽

pp. 483-501 ◽

Cited By ~ 3

Author(s):

Guillermo A. Díaz ◽

Enrique E. Mombello

Keyword(s):

Magnetic Field ◽

Current Density ◽

Finite Cylinder ◽

The Magnetic Field

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On the groundstate energy of tight knots

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2008.0536 ◽

2009 ◽

Vol 465 (2109) ◽

pp. 2761-2783 ◽

Cited By ~ 8

Author(s):

Francesca Maggioni ◽

Renzo L. Ricca

Keyword(s):

Magnetic Field ◽

Magnetic Energy ◽

Energy Levels ◽

Minimum Energy ◽

Internal Field ◽

Exact Expression ◽

Torus Knots ◽

Tube Cross Section ◽

The Magnetic Field ◽

Groundstate Energy

New results on the groundstate energy of tight, magnetic knots are presented. Magnetic knots are defined as tubular embeddings of the magnetic field in an ideal, perfectly conducting, incompressible fluid. An orthogonal, curvilinear coordinate system is introduced and the magnetic energy is determined by the poloidal and toroidal components of the magnetic field. Standard minimization of the magnetic energy is carried out under the usual assumptions of volume- and flux-preserving flow, with the additional constraints that the tube cross section remains circular and that the knot length (ropelength) is independent from internal field twist (framing). Under these constraints the minimum energy is determined analytically by a new, exact expression, function of ropelength and framing. Groundstate energy levels of tight knots are determined from ropelength data obtained by the SONO tightening algorithm. Results for torus knots are compared with previous work, and the groundstate energy spectrum of the first prime knots — up to 10 crossings — is presented and analysed in detail. These results demonstrate that ropelength and framing determine the spectrum of magnetic knots in tight configuration.

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Observing the galactic magnetic field

Symposium - International Astronomical Union ◽

10.1017/s0074180900101251 ◽

1967 ◽

Vol 31 ◽

pp. 375-380

Author(s):

H. C. van de Hulst

Keyword(s):

Magnetic Field ◽

Fair Agreement ◽

Solar Neighbourhood ◽

Galactic Magnetic Field ◽

The Magnetic Field

Various methods of observing the galactic magnetic field are reviewed, and their results summarized. There is fair agreement about the direction of the magnetic field in the solar neighbourhood:l= 50° to 80°; the strength of the field in the disk is of the order of 10-5gauss.

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Evolution of Large-Scale Coronal Structures

International Astronomical Union Colloquium ◽

10.1017/s0252921100024945 ◽

1994 ◽

Vol 144 ◽

pp. 29-33

Author(s):

P. Ambrož

Keyword(s):

Magnetic Field ◽

Field Line ◽

Large Scale ◽

Coronal Magnetic Field ◽

Source Surface ◽

Solar Cycles ◽

Characteristic Relationship ◽

The Magnetic Field ◽

Coronal Structures

AbstractThe large-scale coronal structures observed during the sporadically visible solar eclipses were compared with the numerically extrapolated field-line structures of coronal magnetic field. A characteristic relationship between the observed structures of coronal plasma and the magnetic field line configurations was determined. The long-term evolution of large scale coronal structures inferred from photospheric magnetic observations in the course of 11- and 22-year solar cycles is described.Some known parameters, such as the source surface radius, or coronal rotation rate are discussed and actually interpreted. A relation between the large-scale photospheric magnetic field evolution and the coronal structure rearrangement is demonstrated.

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Emergence of Twisted Magnetic Flux Related Sigmoidal Brightening

International Astronomical Union Colloquium ◽

10.1017/s0252921100064630 ◽

2000 ◽

Vol 179 ◽

pp. 263-264

Author(s):

K. Sundara Raman ◽

K. B. Ramesh ◽

R. Selvendran ◽

P. S. M. Aleem ◽

K. M. Hiremath

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Magnetic Flux ◽

Ultra Violet ◽

Active Regions ◽

Morphological Properties ◽

Energy Storage And Conversion ◽

The Sun ◽

X Rays ◽

The Magnetic Field

Extended AbstractWe have examined the morphological properties of a sigmoid associated with an SXR (soft X-ray) flare. The sigmoid is cospatial with the EUV (extreme ultra violet) images and in the optical part lies along an S-shaped Hαfilament. The photoheliogram shows flux emergence within an existingδtype sunspot which has caused the rotation of the umbrae giving rise to the sigmoidal brightening.It is now widely accepted that flares derive their energy from the magnetic fields of the active regions and coronal levels are considered to be the flare sites. But still a satisfactory understanding of the flare processes has not been achieved because of the difficulties encountered to predict and estimate the probability of flare eruptions. The convection flows and vortices below the photosphere transport and concentrate magnetic field, which subsequently appear as active regions in the photosphere (Rust & Kumar 1994 and the references therein). Successive emergence of magnetic flux, twist the field, creating flare productive magnetic shear and has been studied by many authors (Sundara Ramanet al.1998 and the references therein). Hence, it is considered that the flare is powered by the energy stored in the twisted magnetic flux tubes (Kurokawa 1996 and the references therein). Rust & Kumar (1996) named the S-shaped bright coronal loops that appear in soft X-rays as ‘Sigmoids’ and concluded that this S-shaped distortion is due to the twist developed in the magnetic field lines. These transient sigmoidal features tell a great deal about unstable coronal magnetic fields, as these regions are more likely to be eruptive (Canfieldet al.1999). As the magnetic fields of the active regions are deep rooted in the Sun, the twist developed in the subphotospheric flux tube penetrates the photosphere and extends in to the corona. Thus, it is essentially favourable for the subphotospheric twist to unwind the twist and transmit it through the photosphere to the corona. Therefore, it becomes essential to make complete observational descriptions of a flare from the magnetic field changes that are taking place in different atmospheric levels of the Sun, to pin down the energy storage and conversion process that trigger the flare phenomena.

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On the Configuration of the Magnetic Field of β CrB

International Astronomical Union Colloquium ◽

10.1017/s0252921100080933 ◽

1976 ◽

Vol 32 ◽

pp. 613-622

Author(s):

I.A. Aslanov ◽

Yu.S. Rustamov

Keyword(s):

Magnetic Field ◽

Field Strength ◽

Radial Velocity ◽

Magnetic Field Strength ◽

Complex Shape ◽

Rotation Period ◽

Field Variation ◽

Magnetic Field Variation ◽

Secular Variations ◽

The Magnetic Field

SummaryMeasurements of the radial velocities and magnetic field strength of β CrB were carried out. It is shown that there is a variability with the rotation period different for various elements. The curve of the magnetic field variation measured from lines of 5 different elements: FeI, CrI, CrII, TiII, ScII and CaI has a complex shape specific for each element. This may be due to the presence of magnetic spots on the stellar surface. A comparison with the radial velocity curves suggests the presence of a least 4 spots of Ti and Cr coinciding with magnetic spots. A change of the magnetic field with optical depth is shown. The curve of the Heffvariation with the rotation period is given. A possibility of secular variations of the magnetic field is shown.

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